Open AccessBook
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TLDR
The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.Abstract:
Preface. Acknowledgments. Introduction. Signals, Systems, and Transformations. Wigner Distributions and Linear Canonical Transforms. The Fractional Fourier Transform. Time-Order and Space-Order Representations. The Discrete Fractional Fourier Transform. Optical Signals and Systems. Phase-Space Optics. The Fractional Fourier Transform in Optics. Applications of the Fractional Fourier Transform to Filtering, Estimation, and Signal Recovery. Applications of the Fractional Fourier Transform to Matched Filtering, Detection, and Pattern Recognition. Bibliography on the Fractional Fourier Transform. Other Cited Works. Credits. Index.read more
Citations
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Journal ArticleDOI
Improved homomorphic filtering using fractional derivatives for enhancement of low contrast and non-uniformly illuminated images
TL;DR: The proposed scheme outperforms the existing state-of-the-art techniques by providing better image visual quality and image information in terms of average PSNR and entropy values.
Journal ArticleDOI
A convolution-based fractional transform
TL;DR: A generalized framework defining a class of fractional transforms based on the convolution algorithm of discrete fractional Fourier transform and gyrator transform is proposed, which can be implemented by an optical 4f system with phase-only filtering easily and can be employed for different computational tasks of information processing.
Journal ArticleDOI
Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions
TL;DR: Fractional Fourier, Hartley, cosine and sine number-theoretic transforms are developed and it is shown that fast algorithms applicable to ordinary NTT can also be used to compute the proposed FrNTT.
Proceedings ArticleDOI
Analysis tools for computational imaging systems
TL;DR: The Ambiguity Function (AF), traditionally used for the design of radar waveforms, plays an important role in computational imaging systems and the Wigner Distribution (WD) is related to the AF and provides a concise analysis of the point spread functions (PSF) of imaging systems over defocus.
Book ChapterDOI
Eigenfunctions of the Linear Canonical Transform
Soo-Chang Pei,Jian-Jiun Ding +1 more
TL;DR: In this article, the eigenfunctions and eigenvalues of the linear canonical transform (LCT) are discussed, and the style of the LCT is closely related to the parameters {a, b, c, d} of LCT.